Succinct Representation of Labeled Graphs

  • Jérémy Barbay
  • Luca Castelli Aleardi
  • Meng He
  • J. Ian Munro
Conference paper

DOI: 10.1007/978-3-540-77120-3_29

Part of the Lecture Notes in Computer Science book series (LNCS, volume 4835)
Cite this paper as:
Barbay J., Castelli Aleardi L., He M., Munro J.I. (2007) Succinct Representation of Labeled Graphs. In: Tokuyama T. (eds) Algorithms and Computation. ISAAC 2007. Lecture Notes in Computer Science, vol 4835. Springer, Berlin, Heidelberg

Abstract

In many applications, the properties of an object being modeled are stored as labels on vertices or edges of a graph. In this paper, we consider succinct representation of labeled graphs. Our main results are the succinct representations of labeled and multi-labeled graphs (we consider vertex labeled planar triangulations, as well as edge labeled planar graphs and the more general k-page graphs) to support various label queries efficiently. The additional space cost to store the labels is essentially the information-theoretic minimum. As far as we know, our representations are the first succinct representations of labeled graphs. We also have two preliminary results to achieve the main results. First, we design a succinct representation of unlabeled planar triangulations to support the rank/select of edges in ccw (counter clockwise) order in addition to the other operations supported in previous work. Second, we design a succinct representation for a k-page graph when k is large to support various navigational operations more efficiently. In particular, we can test the adjacency of two vertices in \(O(\lg k\lg\lg k)\) time, while previous work uses O(k) time (10; 14).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Jérémy Barbay
    • 1
  • Luca Castelli Aleardi
    • 2
  • Meng He
    • 1
    • 3
  • J. Ian Munro
    • 1
  1. 1.Cheriton School of Computer Science, University of WaterlooCanada
  2. 2.LIX (Ecole Polytechnique, France) and, CS Department (Université Libre de BruxellesBelgium
  3. 3.School of Computer Science, Carleton UniversityCanada

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